Markov processes, semigroups, and generators / Vassili N. Kolokoltsov.

Format:

Book

Author/Creator:

Kolokolʹt︠s︡ov, V. N. (Vasiliĭ Nikitich)

Series:

De Gruyter studies in mathematics ; 38.

De Gruyter studies in mathematics, 0179-0986 ; 38

Language:

English

Subjects (All):

Markov processes.

Semigroups.

Group theory--Generators.

Group theory.

Physical Description:

1 online resource (448 p.)

Edition:

1st ed.

Place of Publication:

Berlin ; New York : De Gruyter, c2011.

Language Note:

English

Summary:

Markov processes represent a universal model for a large variety of real life random evolutions. The wide flow of new ideas, tools, methods and applications constantly pours into the ever-growing stream of research on Markov processes that rapidly spreads over new fields of natural and social sciences, creating new streamlined logical paths to its turbulent boundary. Even if a given process is not Markov, it can be often inserted into a larger Markov one (Markovianization procedure) by including the key historic parameters into the state space. This monograph gives a concise, but systematic and self-contained, exposition of the essentials of Markov processes, together with recent achievements, working from the "physical picture" - a formal pre-generator, and stressing the interplay between probabilistic (stochastic differential equations) and analytic (semigroups) tools. The book will be useful to students and researchers. Part I can be used for a one-semester course on Brownian motion, Lévy and Markov processes, or on probabilistic methods for PDE. Part II mainly contains the author's research on Markov processes. From the contents: Tools from Probability and Analysis Brownian motion Markov processes and martingales SDE, ψDE and martingale problems Processes in Euclidean spaces Processes in domains with a boundary Heat kernels for stable-like processes Continuous-time random walks and fractional dynamics Complex chains and Feynman integral

Contents:

pt. 1. Introduction to stochastic analysis

pt. 2. Markov processes and beyond.

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9786613166333

9781283166331

128316633X

9783110250114

311025011X

OCLC:

723945552